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Conditioning of Quantum Open Systems

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Encyclopedia of Systems and Control

Abstract

The underlying probabilistic theory for quantum mechanics is non-Kolmogorovian. The time-order in which physical observables are measured will be important if they are incompatible (non-commuting). In particular, the notion of conditioning needs to be handled with care and may not even exist in some cases. Here we layout the quantum probabilistic formulation in terms of von Neumann algebras and outline conditions (non-demolition properties) under which filtering may occur.

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Bibliography

  • Accardi L, Frigerio A, Lewis JT (1982) Quantum stochastic processes. Publ Res Inst Math Sci 18(1):97–133

    Article  MathSciNet  Google Scholar 

  • Belavkin VP (1980) Quantum filtering of Markov signals with white quantum noise. Radiotechnika i Electronika 25:1445–1453

    Google Scholar 

  • Bouten L, van Handel R, James MR (2007) An introduction to quantum filtering. SIAM J Control Optim 46:2199–2241

    Article  MathSciNet  Google Scholar 

  • Hudson RL, Parthasarathy KR (1984) Quantum Ito’s formula and stochastic evolutions. Commun Math Phys 93:301

    Article  MathSciNet  Google Scholar 

  • Kadison RV, Ringrose JR (1997) Fundamentals of the theory of operator algebras. Volumes I (Elementary Theory) and II (Advanced Theory). American Mathematical Society, Providence

    Google Scholar 

  • Maassen H (1988) Theoretical concepts in quantum probability: quantum Markov processes. In: Fractals, quasicrystals, chaos, knots and algebraic quantum mechanics, NATO advanced science institutes series C, Mathematical and physical sciences, vol 235. Kluwer Academic Publishers, Dordrecht, pp 287–302

    Google Scholar 

  • Parthasarathy KR (1992) An introduction to quantum stochastic calculus. Birkhauser, Basel

    Book  Google Scholar 

  • Protter P (2005) Stochastic integration and differential equations, 2nd edn. Springer, Berlin Heidelberg

    Book  Google Scholar 

  • van Handel R (2007) Filtering, stability, and robustness. Ph.D. Thesis, California Institute of Technology

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Physics, Aberystwyth University, Aberystwyth, Wales, UK

    John Gough

Authors
  1. John Gough
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Correspondence to John Gough .

Editor information

Editors and Affiliations

  1. Electrical and Computer Engineering, Boston University, Boston, MA, USA

    John Baillieul

  2. Automation and Control Solutions, Honeywell, Golden Valley, MN, USA

    Tariq Samad

Section Editor information

  1. Research School of Electrical, Energy and Materials Engineering, Australian National University, Canberra, ACT, Australia

    Ian R. Petersen

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Gough, J. (2020). Conditioning of Quantum Open Systems. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_100165-1

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  • DOI: https://doi.org/10.1007/978-1-4471-5102-9_100165-1

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  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-5102-9

  • Online ISBN: 978-1-4471-5102-9

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